Experiment 6: Interferometers Nate Saffold [email protected] Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 NOTE: No labs and no lecture next week! Outline ● The physics behind: ● EM waves ● EM in medium: reflection and refraction ● Interferometry: ● Michelson interferometer ● Fabry-Perot interferometer ● The experiment: ● Introducing the apparati ● Determine the wavelength of He-Ne laser separately for each interferometer. ● Measure the index of refraction of air and glass. PHYS 1493/1494/2699: Exp. 6 – Interferometers 3 Electromagnetic waves ● Electromagnetic wave = oscillating electric and magnetic fields ● An EM wave propagates in vacuum at the speed of light ● Electric and magnetic fields are always perpendicular to each other (James Clerk Maxwell… Pretty smart guy…) PHYS 1493/1494/2699: Exp. 5 – Polarization and Interference 4 Interference ● An essential property of waves is the ability to get combined with other waves ● The result of this superposition can lead to a wave with greater or smaller amplitude ● This phenomenon is called interference Maxima superimposed Maxima superimposed to minima to maxima They cancel out They add to each other PHYS 1493/1494/2699: Exp. 5 – Polarization and Interference 5 EM waves and interference ● In this lab we will study the wave properties of light and in particular interference ● EM waves can superimpose in a constructive or destructive way Constructive 1 ∆` = m + λ 2 Destructive✓ ◆ PHYS 1493/1494/2699: Exp. 6 – Interferometers 6 EM waves and interference ● As a result, when two different EM waves are superimposed they will some times overlap constructively, some times destructively and most often something in between ● The typical interference pattern therefore looks like: Constructive Something in between Destructive PHYS 1493/1494/2699: Exp. 6 – Interferometers 7 EM in medium ● Electric and magnetic fields in medium are different from those in vacuum ● Microscopic explanation: a dielectric material (insulator) can be polarized and hence change its own charge distribution. This changes the EM fields within the medium itself ● Macroscopic description: one defines an electric displacement field: Relative permittivity Electric displacement For the most common dielectric Polarizability materials electric displacement is Susceptibility of proportional to applied electric field the medium PHYS 1493/1494/2699: Exp. 6 – Interferometers 8 EM in medium ● In general, electromagnetism in a medium is different from that in a vacuum ● Maxwell’s equations are different: They look pretty similar to me! PHYS 1493/1494/2699: Exp. 6 – Interferometers 9 Refraction ● Question: if the behavior of EM waves is different from vacuum to medium, what does this cause? ● Refraction: bending of light when passing from a medium to another (e.g. vacuum to air, air to glass, etc.) PHYS 1493/1494/2699: Exp. 6 – Interferometers 10 Refraction ● The behavior of light rays at an interface between two materials is described by the Snell’s Law: PHYS 1493/1494/2699: Exp. 6 – Interferometers 11 Optical path length ● Question: what actually is an index of refraction? ● Since Maxwell’s equations are different the speed of light in a medium is different! with: c = speed of light in vacuum v = speed of light in medium ● Consequence: EM waves originating from the same source but traveling in different media (i.e. different indices of refraction) over the same physical distance, have different optical path lengths. PHYS 1493/1494/2699: Exp. 6 – Interferometers 12 Optical path length (OPL) EM wave traveling in vacuum EM wave traveling in a medium ● Two ways to change OPL = ● Change physical distance (obviously) ● Change index of refraction (i.e. put it in a different medium). PHYS 1493/1494/2699: Exp. 6 – Interferometers 13 OPL in different mediums ● To study interference we only care about the phase difference between waves (i.e. the number of extra wavelengths that a wave travels) ● Let’s consider two waves traveling in two boxes of side L but filled with two different media (n1 and n2): ● The number of wavelengths contained in each box will be: ● Consequently, the number of extra wavelengths is: Number of extra wavelengths Difference in index of refraction between two paths PHYS 1493/1494/2699: Exp. 6 – Interferometers 14 Interferometry ● Interferometry uses the interference of two rays generated from the same coherent source but having different path lengths ● The main idea is: 1. Start with the same coherent source (same , polarization, phase ) 2. Direct the two beams through different paths with path length difference equal to 3. Allow the beams to meet up again at some future point ● The two waves can now make constructive or destructive interference depending if: (Constructive interference) (Destructive interference) PHYS 1493/1494/2699: Exp. 6 – Interferometers 15 Michelson Interferometer ● Michelson (1881): invented it to measure the speed of the earth relative to the “ether”… and he didn’t find anything… sad story… Albert, there is no ether… Told you… ● Idea: 1. Split single beam into two, then recombine. 2. Observer sees interference patterns projected onto a small screen. 3. By moving one of the mirrors, the observer can change the path length difference . The consequence is a shift in the interference pattern. PHYS 1493/1494/2699: Exp. 6 – Interferometers 16 Michelson Interferometer Viewing screen Interference pattern appears here Beam splitter Movable LASER mirror M1 Common coherent source OPL for beam 1 OPL for beam 2 Fixed mirror M2 PHYS 1493/1494/2699: Exp. 6 – Interferometers 17 Michelson Interferometer (on steroids…) ● Michelson interferometers can be pretty large… LIGO @ Hanford Site, Washington VIRGO @ Cascina, Italy Cost ~ 620 million dollars Cost ~ 100 million euros Length ~ 4 km Length ~ 3 km ● These guys are so precise that can be used to detected minuscule space-time variations due to gravitational waves PHYS 1493/1494/2699: Exp. 6 – Interferometers 18 Michelson Interferometer (on steroids…) ● As you probably heard from the news the LIGO interferometer was a huge success! ● On September 14th, 2015 at 09:50:45 UTC they recorded the very first signal coming from a gravitational wave going through the Earth ● This signal most likely came from two black holes with ~30 solar masses each merging together 1.3 billions years ago! ● Quite remarkable for ‘just’ an interferometer… PHYS 1493/1494/2699: Exp. 6 – Interferometers 19 Fabry-Perot Interferometer ● Same idea: split beam and then recombine. ● However, instead of splitting the beam just once, it splits many times using mirrored cavity. ● Each reflection adds a small difference in path length, ● The final result is a circular interference pattern ● Main advantage: the fringes are brighter and well distinguishable PHYS 1493/1494/2699: Exp. 6 – Interferometers 20 Condition for bright spots (constructive) ● The condition for the presence of bright spots is the same for both the previous interferometers ● Suppose we start with the two beams in phase and look at the position of a bright spot, then: 1. Modify one of the two path lengths bright spots will not be bright spots anymore 2. They will be bright spots again when the total path length difference is λ 3. This will happen again at 2λ, 3λ, etc. ● In general, if we change one of the paths by dm, in order to have a bright spot back in its original position we must have: PHYS 1493/1494/2699: Exp. 6 – Interferometers 21 The Experiment PHYS 1493/1494/2699: Exp. 6 – Interferometers 22 Goals ● In this experiment you will use both the Michelson and the Fabry-Perot interferometers ● Fabry-Perot Interferometer: ● Measure the wavelength of the He-Ne laser ● Michelson Interferometer: ● Measure the wavelength of the He-Ne laser ● Measure the index of refraction of air (nair). ● Measure the index of refraction of glass (nglass). PHYS 1493/1494/2699: Exp. 6 – Interferometers 23 Fabry-Perot (FP) interferometer: setup Move this guy = change in Adjustable Movable Converging lens mirror path length = change mirror interference pattern Viewing Screen Circular fringes appear here LASER Micrometer knob Allows you to move the mirror by very small fractions of a mm PHYS 1493/1494/2699: Exp. 6 – Interferometers 24 How to read a micrometer ● The micrometer will allow you to move one of the two mirrors by very small distance. ● This will shift the interference patter Example: In the Each of these picture you can marks is 1 µm read the 500 µm mark, the 25 µm mark and the knob reads 7 µm. Position = 532 µm Each of these marks is 100 µm PHYS 1493/1494/2699: Exp. 6 – Interferometers 25 FP interferometer: procedure ● Follow directions for FP setup on the lab manual ● A few tips: ● Turning the micrometer knob to move mirrors will cause the fringe pattern to change. ● Fringes move really fast! Do this with the help of a lab partner. ● Measure at least the passing of 20 fringes. The more fringes you measure, the better the measurement! ● Record distance dm that mirror moves and number of fringes passing through a fixed point. ● Repeat measurement 10 times for different dm! PHYS 1493/1494/2699: Exp. 6 – Interferometers 26 FP interferometer: He-Ne wavelength ● Plot dm vs. m (number of fringes): ● For each measurement, extract wavelength λ using above equation. ● Report average: ● Compare to accepted value of 632.8 nm PHYS 1493/1494/2699: Exp. 6 – Interferometers 27 Michelson interferometer: setup Viewing screen LASER Movable mirror Beam splitter Lens Adjustable mirror PHYS 1493/1494/2699: Exp. 6 – Interferometers 28 Michelson interferometer: procedure ● Remove lens in front of the laser. ● Follow procedures as in lab manual. ● Tips for setup: ● For best results, make sure the two beams are almost exactly on top of each other before placing lens in front of laser! ● Same tips as in FP apply to Michelson. ● Measurement of He-Ne laser wavelength: ● Same procedure: Measure fringes vs distance of movable mirror. Take 10 trials. ● Report ● Compare to accepted value and Fabry-Perot Interferometer.